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math.NA2026
Randomized Neural Networks for Integro-Differential Equations with Application to Neutron Transport
Haoning Dang, Fei Wang, Yifan Chen +3
Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral op…
math.NA2021
Solving and Learning Nonlinear PDEs with Gaussian Processes
Yifan Chen, Bamdad Hosseini, Houman Owhadi +1
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identificat…
math.NA2020
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data
Yifan Chen, Thomas Y. Hou
There is an intimate connection between numerical upscaling of multiscale PDEs and scattered data approximation of heterogeneous functions: the coarse variables selected for derivi…